On generalized choice and coloring numbers
Zden\v{e}k Dvo\v{r}\'ak, Jakub Pek\'arek, Jean-S\'ebastien, Sereni
TL;DR
This paper investigates the relationship between coloring numbers and choosability in graphs, extending known results to more general settings with relaxed assumptions using a graph parameter.
Contribution
It generalizes the relationship between coloring number and choosability by incorporating a graph parameter to relax assumptions on color classes.
Findings
Established bounds relating coloring number and choosability in generalized settings.
Extended Alon's results to broader classes of graphs with relaxed assumptions.
Provided new insights into graph coloring parameters and their interactions.
Abstract
A well-known result of Alon shows that the coloring number of a graph is bounded by a function of its choosability. We explore this relationship in a more general setting with relaxed assumptions on color classes, encoded by a graph parameter.
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